Transformations and Soliton Solutions for a Variable-coefficient Nonlinear Schrödinger Equation in the Dispersion Decreasing Fiber with Symbolic Computation

Article type: Research Article

Authors: Zeng, Zhi-Fang^a | Liu, Jian-Guo^b | Jiang, Yan^{c; *; †} | Nie, Bin^d

Affiliations: [a] Department of Basic, Jiangxi Vocational and Technical College of Communication, JiangXi 330013, China. [email protected] | [b] College of Computer, Jiangxi University of Traditional Chinese Medicine, JiangXi 330004, China | [c] ChongQing JianZhu College, ChongQing 400072, China. [email protected] | [d] College of Computer, Jiangxi University of Traditional Chinese Medicine, JiangXi 330004, China

Correspondence: [†] Address for correspondence: ChongQing JianZhu College, ChongQing 400072, China.

Note: [*] Project 61562045 supported by National Natural Science Foundation of China.

Abstract: Describing the dispersion decreasing fiber, a variable-coefficient nonlinear Schrödinger equation is hereby under investigation. Three transformations have been obtained from such a equation to the known standard and cylindrical nonlinear Schrödinger equations with the relevant constraints on the variable coefficients presented, which turn out to be more general than those previously published in the literature. Meanwhile, several families of exact dark-soliton-like and bright-soliton-like solutions are constructed. Also, we obtain some similarity solutions, which can be illustrated in terms of the elliptic and the second Painlevé transcendent equations.

Keywords: symbolic computation, nonlinear Schrödinger equation, similarity solutions, soliton-like solutions

DOI: 10.3233/FI-2016-1355

Journal: Fundamenta Informaticae, vol. 145, no. 2, pp. 207-219, 2016